President Trump floated a “potential path to citizenship” for H1-B visa holders in an early Friday morning tweet, as the partial government shutdown is set to become the longest shutdown on record.

It’s unclear what Mr. Trump meant exactly, as simplifying a path to citizenship for such visa holders would almost certainly require approval from Congress, and the White House has made no such suggestion in its latest border security funding proposal, or any other public offer.

“H1-B holders in the United States can rest assured that changes are soon coming which will bring both simplicity and certainty to your stay, including a potential path to citizenship,” Mr. Trump tweeted. “We want to encourage talented and highly skilled people to pursue career options in the U.S.”

The H-1B visa, under the Immigration and Nationality Act, lets U.S. employers temporarily employ foreign workers with at least a bachelor’s degree for speciality occupations. H-1B visa holders can apply for a green card to obtain permanent residency — but even a green card does not equate to citizenship.

Mr. Trump has expressed openness to a broader immigration overhaul, but has insisted that he first wants funding for a concrete or steel wall or barrier, along with funding for technology and personnel to handle the situation at the border. It’s unclear what prompted Mr. Trump’s tweet.

During the campaign, Mr. Trump proposed increasing the prevailing wage paid to H-1B visa holders in an effort to force companies to give entry-level jobs to an existing pool of unemployed workers in the U.S., instead of bringing in cheaper workers from overseas.

“This will improve the number of black, Hispanic and female workers in Silicon Valley who have been passed over in favor of the H-1B program,” the Trump campaign wrote in an August 2015 immigration platform.

Meanwhile, the president continues to put his immigration agenda front and center. The president has threatened to call a national emergency if Congress doesn’t reach an agreement to fund his border wall.

“If this doesn’t work out, I probably will do it, I would almost say definitely,” Mr. Trump told reporters Thursday on his way to the southern border, adding later, “If we don’t make a deal, I would say 100 percent but I don’t want to say 100 percent.”